1. Introduction

A strategic alliance may be defined as a cooperative arrangement between two or more independent firms that exchange or share resources for competitive advantage. Since the 1980s, strategic alliances have been widely discussed (Porter and Fuller, 1986; Harrigan and Newman, 1990; Auster, 1994) and hundreds of papers have been published on this issue. The essential motives of strategic alliances are 'synergy effects', as represented in the following equation:

where V() denotes the satisfaction (or value) function and S_k denotes the kth alliance firm. When Equation (1) is satisfied, alliance firms can share more satisfaction level than their original states through strategic alliances.

Since some firms rush into strategic alliances without appropriate preparation or planning to choose the correct partners and resource allocation, these alliances often fail (Dacin et al, 1997). It can be seen that the questions above are usually complex and diversified, that is, with each firm's goals, culture, and resources being different, the best alliance partners and resource allocation are dissimilar. This paper proposes a model that can determine the best partner choice and the optimal resource allocation for strategic alliances.

Although the criteria for choosing correct partners have been widely proposed, some being as complementary strengths, commitment, coordination, and compatible goals (Gerlinger, 1991; Brouthers et al, 1995; Yoshino and Rangan, 1995; Arino and Abramov, 1997), these papers seem to ignore the issue of resource allocation. It is clear that only by using these alliance resources effectively can synergy effects arise. On the other hand, the issue of resource allocation (Robinson et al, 1992; Bretthauer and Shetty, 1995, 1997; Lai and Li, 1999) also has been discussed for a long time in operations research and the purpose of resource allocation is concerned with obtaining the maximum profits for the enterprise and satisfaction/utility for the customer with limited resources. It is reasonable to incorporate both the concepts to overcome the problems of choosing alliance partners and resource allocation.

In order to overcome these problems and derive a useful model, several issues should be considered. First, since the problem of choosing alliance partners is part of the combinatorial problem, the scaling problem should be considered. Second, these objectives in a firm and the satisfaction in an alliance should be precisely measured and calculated. Third, based on the principle of the market mechanism, the unit price of resources should be incorporated into the model. It is clear that the optimal resource allocation varies with the different unit price of resources. Finally, because the real-world problems usually have the restriction of integer type, the integer resource allocation solutions should be supported.

In this paper, we propose the fuzzy multi-objective dummy programming model to satisfy these claims above and provide the best alliance cluster and the optimal resource allocation combinations. In addition, two types of strategic alliances, joint ventures and mergers and acquisitions (M&A), are demonstrated to choose the best alliance partners and allocate the optimal alliance resources in a numerical example using the proposed method. On the basis of the numerical results, we can conclude that the proposed method can provide the optimal alliance cluster and satisfaction for alliance partners.

The rest of this paper is organized as follows: The review of strategic alliances is discussed in Section 2. De Novo programming is proposed in Section 3. Fuzzy multi-objective dummy programming is derived in Section 4. In Section 5, a numerical example is used to illustrate the proposed method by considering joint ventures and M&A. Section 6 presents a discussion of implementation, and conclusions are in the last section.

2. The review of strategic alliances

A strategic alliance may be defined as a cooperative arrangement between two or more independent firms that exchange or share resources for competitive advantage. From the resource-based views (Wernerfelt, 1984; Barney, 1991; Grant, 1991; Barney, 2001; Barney et al, 2001), valuable resources which firms do not own are the motive for strategic alliances. Many classifications for valuable resources have been proposed (Miller and Shamsie, 1996), and these resources can generally be classified into tangible (eg financial and technological) and intangible (eg knowledge-based and managerial) resources.

In order to acquire competitive advantage and the ability to respond quickly in a dynamic environment, firms should consider how to construct and extend limited resources to develop a capability for sustainable competitive advantage (Teece et al, 1997). Through strategic alliances, firms can gain their partners' complementary resources to enhance or reshape their internal processing to create synergies and competitive advantage within a market (Nohria and Garcia-Pont, 1991). According to the different degrees of vertical integration or independence, various forms of strategic alliances can be represented using the following spectrum (Lorange and Roos, 1992) (Figure 1).

Figure 1.

Spectrum of strategic alliances.

Full figure and legend (12K)

However, the questions arise: 'How can we choose the correct partners?' and 'How can we allocate these valuable resources?' It is of no doubt that choosing the correct partners is the first step in entering into a successful strategic alliance, and this process requires careful screening, which can be a time-consuming process. Furthermore, it is more important that firms can gain nothing unless they can use their newly-acquired resources effectively. In other words, the optimization of resource allocations is the key to whether firms can create synergies and obtain competitive advantage. In this paper, we demonstrate two types of strategic alliances, joint ventures and M&A, to choose the best alliance partners and determine the optimal resource allocation for the alliance.

Joint ventures can be defined as the sharing of assets, risks, profits or investment projects by more than one firm or an alliance cluster (Harrigan, 1985; Kough, 1988, 1991). Joint ventures can be considered as a mechanism to reduce the transaction costs incurred when acquiring other firms (Hennart and Reddy, 1997). Over the time that the concept of joint ventures has been in practice, the number of joint ventures in the US grew by 423% over the period 1986–1995 (Hitt et al, 1997). If the strategic alliance is a joint venture, a firm can share the surplus resources with alliance partners to increase total alliance satisfaction. We can depict the above concepts in Figure 2 to display the processes of joint ventures.

Figure 2.

The concept of joint ventures.

Full figure and legend (14K)

Note that based on the concepts above, it is obvious that the equilibrium of joint ventures is where all alliance partners have the same satisfaction.

On the other hand, M&A is the extreme situation of strategic alliance, where two or more firms form one enterprise and that enterprise can use all partners' resources to optimize the goals of the organization (Whitelock and Rees, 1993). This means that the enterprise may cancel some products in firms for the alliance to optimize the overall alliance satisfaction. A firm will favour M&A over joint ventures when the assets it needs are not commingled with other unneeded assets within the firm that holds them, and hence they can be acquired by buying the firm or a part of it (Hennart and Reddy, 1997). Using Figure 3, we can present the processes of M&A to optimize the alliance satisfaction.

Figure 3.

The concept of mergers and acquisitions.

Full figure and legend (9K)

The main difference between joint ventures and M&A is that joint ventures emphasize the sharing of surplus resources to optimize alliance satisfaction (ie alliance members still develop their own products), whereas M&A is concerned only with optimizing the overall alliance satisfaction. In order to discuss the ways of allocating optimal alliance resources in a market mechanism, De Novo programming is proposed in the next section.

3. De Novo programming

Traditionally, the resource allocation problem (Hackman and Platzman, 1990) can be considered to maximize the following knapsack problem:

where matrix C and vector x denote given resource parameters, matrix A denotes the technological coefficient and b denotes the maximum limited resource portfolio. It can be seen that the key to optimizing objective functions depends on the appropriate resource parameters and resource portfolio. In practice, however, it is usually hard to achieve aspiration levels due to the inappropriate resource allocation.

In addition, although it is rational to allocate resources using the equation above in a hierarchical system, when the resource allocation problem is under market-based systems, the factor of a resource's unit price should be considered and the traditional methods are no longer suitable. In order to achieve the optimal resource allocation, De Novo programming is proposed to resolve this problem.

De Novo programming was proposed by Zeleney (1981, 1986) to redesign or reshape given systems to achieve an aspiration/desired level. Later, various issues, such as considering fuzzy coefficients (Li and Lee, 1990), optimum-path ratios (Shi, 1995), and 0–1 programming problem (Kim et al, 1993), have been proposed. The original idea of De Novo programming was that productive resources should not be engaged individually and separately because resources are not independent. By releasing various constraints, De Novo programming attempts to break the limitations in achieving the aspiration/desired solution.

The procedures of De Novo programming can be described as follows:

1. Find the aspiration level vector (z^u) according to the following equation:
   
   
   
   
   where V=pA denotes the unit cost vector, p is the resource's unit price vector and B=pb denote the total budget.
2. Identify the minimum budget B^* and its corresponding resource allocation (x^* and b^*) with the aspiration level such as
   
   
   
   
3. Using the optimum-path ratio (r) to obtain the final solution (z, x and b)
   
   
   
   
   where r=B/B^*

Since De Novo programming deals with the problem of resource allocations in one system, the problem of choosing partners and allocating alliance resources still exists. Next, we propose the fuzzy multi-objective dummy programming model to provide the best alliance cluster and the optimal resource allocation combinations in the alliance.

4. Fuzzy multiple objective dummy programming

In this section, we first describe the concepts of fuzzy sets so that the readers can more easily understand the proposed method. However, we do not present all the issues about fuzzy sets and restrict the relative contents to this paper. The concepts of fuzzy sets were proposed to extend classical crisp set to consider the certain degree in the interval [0,1]. Since real-world problems are usually partly true and partly false, fuzzy sets are widely employed to deal with the problems of uncertainty (especially the problems of subjective uncertainty).

In order to present the degree of uncertainty, the degree of membership is developed. Given fuzzy set à of universe Y, the membership function of set A can be defined as

where _Ã(y)=1 if y is totally in Ã, _Ã(y)=0 if y is not in Ã, 0<_Ã(y)<1 if y is partly in Ã.

Usually, the fuzzy set à can be represented using the triangular or trapezoidal fuzzy number. Consider the following example in Figure 4, three fuzzy sets, short, average, and tall, are used to present the degree of height. The fuzzy sets of short and tall can be represented using the trapezoidal fuzzy numbers (140, 140, 150, 165) and (175, 190, 190, 190), respectively. The fuzzy set of Average can be represented using the triangular number (160, 170, 180).

Figure 4.

The concepts of fuzzy set.

Full figure and legend (8K)

Next, in order to measure the satisfaction of strategic alliances, the concept of fuzzy sets is used. The conventional fuzzy programming problem (Zimmermann, 1978) can be represented as follows:

where and are the fuzzification of and , respectively. Then the satisfaction for each objective aspiration level can be represented using the following linear membership function

where z_q^u and z_q^l are the aspiration level and the minimum level, respectively and d_q denotes the subjective perception of the minimum tolerant constants which usually assume d_q=z_q^u-z_q^l and the corresponding relation can also be depicted as shown in Figure 5.

Figure 5.

The membership function for z_q.

Full figure and legend (5K)

Note that the minimum (maximum) level z_q^l (z_q^u) can be obtain by solving each single objective mathematical programming model. For example, of the two-objective mathematical programming problem, the first minimum (maximum) level z₁^l (z₁^u) can be obtained by solving the following model:

By letting (z)=min{(z_q)|q=1, ..., Q} denotes the overall satisfaction level, while u=1-(z) denotes the overall regret level. We can model two strategic alliance types, joint ventures and M&A, as follows. Without loss of generalization, in the maximum problem, if there are I firms in an alliance cluster and J firms are candidates to be chosen to enter the alliance, then, according to the concept of joint ventures, we can propose the joint venture model as follows:

4.1. Joint ventures model

where n_i, n_j and p_i, p_j denote slack and surplus variables in alliance cluster and candidate partners, respectively, S_j denotes the dummy variable in the jth firm where 1 indicates entery into strategic alliance, e denotes the unused budget which can be ignored in resource dividable system but cannot be ignored in the resource undividable system. Note that in the minimum problem, we can substitute un_i/(z_i^u-z_i^l) and uS_jn_j/(z_j^u-z_j^l) with up_i/(z_i^u-z_i^l) and uS_jp_j/(z_j^u-z_j^l) that is, we can ignore p_i and p_j when dealing with the maximum problem.

On the other hand, the M&A model can also be derived based on Figure 3 in Section 2 to obtain the optimal alliance satisfaction as follows:

4.2. M&A model

On the basis of the two models above, we can conclude the advantages of the proposed method as follows. First, we can easily choose the correct alliances partners by setting a dummy variable, S, using the conventional mathematical programming methods or other heuristic algorithms such as genetic algorithms or simulated annealing. Second, using the concept of fuzzy sets, we can easily measure the alliance satisfaction. Next, by incorporating the concept of De Novo programming, the unit price of the resources can be considered in the proposed models.

Besides, if both the technological coefficients and resource portfolio are undividable, the programming can easily be rewritten in the form of the integer programming problem. Since several algorithms, such as branch and bound algorithm (Bretthauer and Shetty, 1995), linear knapsack method (Mathur et al, 1986; Hochbaum, 1995), and dynamic programming algorithm (Glover, 1975), can be used to solve this integer fuzzy multi-objective dummy programming problem, it is more suitable for dealing with the real-world alliance problems. In order to demonstrate the advantages of the proposed method, a numerical example is employed to display the satisfaction results in both the joint ventures and the M&A cases.

5. Numerical example

Strategic alliances are widely adopted by firms to increase competitive advantage in practice. By exchanging or sharing alliance resources, each alliance firm can obtain more satisfaction level than their original satisfaction level. However, since every firm has its own products, objective functions, constraints, and capital, it is hard for firms to consider the best alliance partners. In this section, the joint ventures and the M&A strategies are considered here to provide the sound solutions, using the proposed method.

Assume that an Enterprise considers entering into strategic alliances with five other candidate firms. For simplicity, these six firms all produce two products (x and y) and have the same objectives, revenue (R), quality (Q) and satisfaction (S), and production constraints, material (M), channel (C), promotion (P) and expert (E). Extra information, including technology coefficients, and capitals in all six firms can be described as shown in Table 1.

Table 1 - Objective and production information about six firms.

Full table

For Enterprise, the aspiration level can be described to solve the following equations:

In order to increase the enterprise's objective values, the joint ventures strategy is considered to choose the best alliance partners. In addition, the corresponding resource allocation should also be determined. Using Equation (8), we can obtain the best alliance cluster and the optimal resource allocation in the case of joint ventures as shown in Table 2.

Table 2 - The alliance partners and resource allocation in joint ventures.

Full table

By removing the factor of alliance partners, we can obtain the optimal resource allocation in Enterprise and Firm 3 using the fuzzy multi-objective dummy programming model as shown in Tables 3 and 4.

Table 3 - The optimal resource allocation in enterprise.

Full table

Table 4 - The optimal resource allocation in Firm 3.

Full table

Comparing Tables 2, 3 and 4, Firm 3 shares redundant resource with Enterprise to increase the alliance satisfaction. It is clear that the alliance satisfaction is larger than the average satisfaction, that is, satisfying the following equation:

indicates that due to the emergence of synergy effects, the firms have motives to enter joint ventures. Next, we use the integer M&A model (ie Equations) to obtain the best alliance partners and the optimal resource allocation for the case of M&A as shown in Table 5.

Table 5 - The alliance partners and resource allocation in M&A.

Full table

On the basis of Table 5, it can be seen that the best alliance cluster in M&A is different with joint ventures. However, the synergy effects can also be found using the same mentioned above method to motivate the development of the M&A strategy. Next, we provide in-depth discussions according to the implementations.

6. Discussions

Strategic alliances are widely used in business to obtain synergy effects. These synergy effects may come from economies of scale, economies of scope, learning effects, etc. However, many firms fail in strategic alliances without the sound planning or screening in choosing the correct partners and resource allocations. In this paper, we provide a new method to overcome these problems.

Two types of strategic alliances, joint ventures and M&A, are demonstrated here to present the proposed method. From the numerical examples, it can be seen that in joint ventures, the surplus resources of Firm 3 (ie 5,200-4,930.55=269.45) are shared with Enterprise to increase the alliance satisfaction (from 0.54 to 0.57). This is the reason why Enterprise has the motives to consider the joint venture strategy. The same situation can also be found in the M&A case.

From our implementation, the M&A strategy seems to provide a better satisfaction level than the joint venture strategy. However, this is not necessarily true in practice. Since in our case we do not consider a alliance costs such as coordination cost, control cost, and risk cost, the optimal alliance strategy cannot be determined. The alliance costs between joint ventures and M&A can be described as in Figure 6.

Figure 6.

Alliance costs in joint ventures and M&A.

Full figure and legend (8K)

Since the alliance costs for joint ventures and for M&A are much different, we cannot ignore the effect of alliance costs. It is clear that with considering the different cost functions, the best alliance strategy could be different.

In addition, the most important thing to facilitate strategy alliances may be the issue of how to set the fair sharing criteria. In the joint ventures case, the satisfaction of Firm 3 decreases from 0.65 to 0.57. However, it is impossible for Firm 3 to enter alliances if its satisfaction level in the alliance is lower than its original level. Therefore, the rational way to assign synergy effects in our joint ventures case can be restricted such that (z_e^*)0.43 and (z₃^*)0.65, where (z_e^*) and (z₃^*) denote the true satisfaction level for Enterprise and Firm 3, respectively, after joint ventures. The same way can be used to set the appropriate sharing mechanism for M&A. More discussions about setting the fair sharing criteria can refer to our paper (Huang et al, 2005).

7. Conclusions

The goal of strategic alliances is to create and share the maximum synergy effects among alliance partners. In order to achieve this goal, the correct alliance partners and the appropriate resource allocation are critical. In this paper, the fuzzy multi-objective dummy programming model is proposed to overcome the above problems. On the basis of the numerical results, we can conclude that both the joint ventures and the M&A model can provide the best alliance cluster, the maximum synergy effects, and the optimal alliance satisfaction.

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